Properties.Methods and Procedures to calculate limits and continuity

Sometimes we seem lost through the details when studying a subject. However if we get the big picture it becomes easy to continue studying.  A math topic is structured in concepts, rules or properties and theorems. This is the theoretical part. Then come the applications. The theories are applied in the applications but the procedures and methods are mastered through practice. Knowing some key theories and procedures can help tremendously in the solutions of problems. In this post I will highlight the properties of limits and continuity, the methods and procedures to solve problems.

Properties of limits

The properties of limit show how to calculate the limits of a combination of functions like the sum, the difference, the multiplication and division of functions. It shows also how to calculate the limit of the square root of a function.

Properties of continuous functions

Methods for determining limits

There are three methods that can be used to determine a limit. These methods are: graph, table and algebra. The graph method consists in determining a limit from the graph. The table method consists in calculating the limit to the left and to the right by drawing a table for each one-sided limit. The table allows to see the behavior of the values of f(x) as x gets closer and closer to a fixed value. From there we can conclude if the limit to the right or to the left exists. If the limits from both sides exist and are equal then the limit of the function exists at the given value. The algebra method consists by substituting the value of the independent variable in the function.

Method for determining if a function is continuous

To determine if a function is continuous, we find out if it satisfies the three following conditions:
1) It is defined at a specified point "a"
2) The limit at the point "a" exists
3) The limit of the function at the point "a" is equal to f(a).

If you are interested in learning more about these concepts you can subscribe to this free Introductory Calculus course or this complete course Calculus AB